What is the square root of 149?

Understand the Problem

The question is asking for the square root of the number 149, which is a mathematical operation that finds a number that, when multiplied by itself, gives 149.

Answer

The square root of 149 is approximately $12.2066$.
Answer for screen readers

The square root of 149 is approximately $12.2066$.

Steps to Solve

  1. Identifying the square root operation

To find the square root of a number, you can use either multiplication or a calculator function. The square root of a number $x$ is the number $y$ such that $y^2 = x$.

  1. Applying the square root to 149

To compute the square root of 149, we can either estimate it between two perfect squares or use a calculator.

We know that:

$$ 12^2 = 144 $$

and

$$ 13^2 = 169 $$

Thus, the square root of 149 lies between 12 and 13.

  1. Using a calculator for precision

Using a calculator, we find:

$$ \sqrt{149} \approx 12.206555615733702 $$

This provides a more accurate value for the square root of 149.

The square root of 149 is approximately $12.2066$.

More Information

The square root of 149 is an irrational number. This means it cannot be expressed as a simple fraction. The decimal expansion continues infinitely without repeating, making it non-terminating.

Tips

  • Forgetting that the square root can be irrational: Many may assume that all square roots yield whole numbers, but this is not always true.
  • Not verifying the result: After finding the square root, it's important to square the answer to ensure it equals the original number.
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